Nonlinear controller design and testing for chatter suppression in an electric-pneumatic braking system with parametric variation

Mechanical Systems and Signal Processing 135 (2020) 106401

Contents lists available at ScienceDirect

Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp

Nonlinear controller design and testing for chatter suppression in an electric-pneumatic braking system with parametric variation Xiuheng Wu, Liang Li ⇑, Xiangyu Wang, Xiang Chen, Shuo Cheng State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084, China

a r t i c l e

i n f o

Article history: Received 12 July 2019 Received in revised form 20 August 2019 Accepted 28 September 2019

Keywords: Electric-pneumatic braking system Chatter suppression Adaptive feedforward control High-gain observer Nonlinear control

a b s t r a c t Accurate pressure control is essential for an electric-pneumatic braking system (EPBS). However, component wear and prolonged service can cause EPBS parameters to drift, which results in system chatter with high frequency. Such is a state of nonlinearity and instability that leads to the gradual deterioration of pressure control. Designing a viable controller for the system is challenging as it requires that system nonlinearity, sensor configuration, and computing capacity be considered. This article addresses the issue and presents a 2-step nonlinear control strategy. An LMS-based adaptive feedforward amplitude-phase regulator is first employed to reduce the frequency of the high frequency pressure oscillation to low frequency’s, followed by applying an output feedback controller based on high gain observer to mitigate the low frequency oscillations to realize steady state. A logic rule is designed to ensure that the two controllers work to suppress pressure oscillations of high and low frequencies in coordination. A comprehensive system model is derived to help characterize system nonlinearities and for designing the high gain observer. Numerical and physical validation are executed to demonstrate the feasibility of the strategy and for the performance of the controller design. Experiments results shows that the nonlinear controller can supress the chatter within 0.1 s either in step response or sinusoid tracking when system parameters vary. Ó 2019 Published by Elsevier Ltd.

1. Introduction As the core component for exerting braking force and implementing active stability control for commercial vehicles, electric-pneumatic braking system (EPBS) is vital for ensuring driving safety, especially when a vehicle operates under extreme conditions in which minor braking force fluctuation can lead to dynamic instability [1–3]. In order to obtain substantial control performance, modeling, analysis and precise adjustment are the 3 important directions being explored in this field [3–5]. Nowadays, it is expected EPBS will be a basic module for driverless commercial vehicles given their direct controllability by micro-computers in future [6–8], so research on how to get accurate and stable pressure control of PEBS especial in extreme condition is significant to improve the safety of commercial vehicles. Compressed air as the power-transmitting medium in EPBS are susceptible to working conditions such as temperature and humidity. Moreover, different tubing construction and arrangement also can generate different flow behavior of the ⇑ Corresponding author. E-mail address: [email protected] (L. Li). https://doi.org/10.1016/j.ymssp.2019.106401 0888-3270/Ó 2019 Published by Elsevier Ltd.

2

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401

Nomenclature pr0 Vr0 mar0 pr Vr mar pc0 Vc0 mac0 pc Vc mac n Gar AE dIR dOR cd ps pa R Ta Ar Ar1 Kr Ffr Fv

l AR Cri Cro Gac VS xr xrm xc Kc ep eLp eHp Kp1 Kp2 EPBS LMS PWM FFT LPF HPF SISO MIMO LMI ECU CAN ECU CAN

Initial pressure of the control chamber Initial volume of the control chamber Initial air mass of the control chamber Current pressure of the control chamber Current volume of the control chamber Current air mass of the control chamber Initial pressure of the load chamber Initial volume of the load chamber Initial air mass of the load chamber Current pressure of the load chamber Current volume of the load chamber Current air mass of the load chamber Ideal gas polytropic exponent Mass flow of control chamber Effective orifice area of the equivalent proportional valve PWM duty cycles of the inlet valve PWM duty cycles of the release valves Gas flow coefficient of orifice Pressure of supply air Discharge atmospheric pressure Specific gas constant Absolute temperature Effective area of the control chamber Effective area of the load chamber Stiffness of the relay valve reset spring Friction between the piston and valve body Vertical force Dynamic friction coefficient Effective air flow area of the relay valve Perimeters of the ring-like inlet orifice Perimeters of the ring-like release orifice Mass flow of load chamber Reference volume of the load chamber Displacement of valve piston Center position of valve piston Displacement of the wheel cylinder piston Stiffness of the wheel cylinder reset spring Error vector Low frequency component vector of error High frequency component vector of error Coefficient of proportional controller Proportional coefficients of state feedback controller Electric-Pneumatic Braking System Least Mean Square Pulse Width Modulation Fast Fourier Transform Low pass filter High pass filter Single Input Single Output Multiple Input Multiple Output Linear Matrix Inequality Electronic Control Unit Controller Area Network Electronic Control Unit Controller Area Network

pressed air [9–10]. These omnipresent nonlinearities present a unique challenge EPBS control with desired accuracy. Many significant works in regard to EPBS nonlinearity analysis and modeling are available [10–19] and based on these many methods are proposed to achieve acceptable control performance subject to specific conditions [20–23]. However, few consider

3

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401

the nonlinear behavior induced by the variations of system parameters. For instance, degradation of a relay valve can sway system parameters over a certain time of deployment and negatively impact the characteristics of the EPBS in an unpredictable manner. In the traditional commercial vehicle, the component service life of EPBS is considered in initial design process, and it always runs normally during all service life. But with the development of hybrid power commercial vehicle, in order to obtain the optimal energy consumption, the electro-mechanical braking system, the motor based regenerative braking system and different drive system switch frequently in short time to reach the maximum efficiency of energy transfer, it will increase the working time of EPBS, exacerbate the wear and aging of components [24–26]. So, it is necessary to take the parametric variation leaded by component wear and prolonged service fully into account when designing the controller for it. Driven-by-wire relay valves are the pivotal regulator in EPBS [27]. They convert electronic signal from the brake pedal to pneumatic press to generate braking force in normal operation. To ensure more safety, they adjust the braking force according to the pressure signal received from the brake pedal foot valve when the electronic system is disabled. To provide redundancy and to keep the conversion as linear as possible subject to the influences of many nonlinear factors mentioned above, relay valves must be carefully designed, thus necessarily resulting in considering many state space variables for complex valve design. Given their inherent complexity, relay valves are designed primarily based on steady-state models, the initial parameter can ensure kinetic stable of system. But valve parameters can drift over time over wear and aging of components subject to repeated and prolonged working conditions, rendering EPBS designed with a large state space to display modes of complex nonlinear response that are the coupled state of multiple variables. Limit cycle, torus of two-frequency, and even chaos are typical responses [28]. EPBS in either of these states would chatter in high frequency with deteriorating pressure control performance. Because a compromised relay valve does not indicate its fallacy to natural attrition such as wear overnight, but rather over an extended amount of accumulated service life cycles, it is extremely difficult to foresee EPBS failure. To address this issue, this paper presents a controller design effective in addressing nonlinearities caused by parameter variation to maintain EPBS stability. The design also considers practical engineering needs for the least number of sensors and the cap of the onboard micro-chip’s computing capacity. Valve chatter suppression is controlled following a two-step strategy. An LMS-based adaptive feedforward amplitude-phase regulator is first employed to reduce the frequency of the high frequency pressure oscillation, followed by applying a high gain observer output feedback controller to mitigate the low frequency oscillations to realize steady state. The rest of the paper is organized as follows. Section 2 analyzes the working mechanism of the relay valve and introduces an EPBS system model. EPBS nonlinear behaviors are then investigated by varying valve parameters. Section 3 describes the fundamental principle upon which the chatter suppression controller design is developed. Numerical study and physical testing are performed to validate the presented design in Section 4. Finally, the conclusions are presented in Section 5.

2. Physical principle and EPBS model Fig. 1 shows a general EPBS. The system consists of four components; namely, a control unit, an air supply subsystem, a pressure control valve block and an actuator. The pressure control valve block includes an inlet valve, a release valve, a relay valve and a pressure sensor used for measuring the pressure in the load chamber of the relay valve. The inlet valve and release valve belong to the high-speed switch valve that together are controlled by a PWM (Pulse Width Modulation) signal. The inlet valve inflates the control chamber and the release valve is used to discharge the air. The piston of the relay valve moves axially to realize charging and discharging.

Control Unit

Brake pedal signal Inlet Valve

Air Receiver

Release Valve

Ar Vr pr

mr s

M

Pressure Sensor bottom plug

mr1r xr

Air Supply

control chamber piston

Kc Ac

Fc

Vc m c pc

load chamber

Kr

Pressure Control Valve Block Fig. 1. Schematic of electric-pneumatic braking system.

xc Wheel Cylinder

4

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401

Fig. 2 defines piston position with the corresponding mode of action. At initial position, the action port connects with the release port and the pressure of the wheel cylinder is approximately atmospheric. When the pressure of the control chamber is increased, the relay valve piston tends to move toward to close the release port firstly, then to reach the centre position. While the piston reaches the bottom plug to open the inlet port, the inlet port connects with the action port, allowing the air receiver to transport high pressure air through the load chamber to the actuator. With the increasing of the load chamber’s pressure, the reaction force to the piston leads to the closing of the inlet port and the pressure of the loading chamber stays stabilized, thus the pressure of the control chamber is in a linear relationship with the pressure in the load chamber of the relay valve. As this relationship is correlates with in the braking force, the severity of braking can be controlled by the inlet and outlet valves. At the termination of braking, the release valve opens and the piston moves up rapidly under the actions of the pressure and reset spring, allowing high pressure air in the wheel cylinder to be discharged. 2.1. Mathematical model The mechanism depicted in Fig. 1 along with the system variables defined therein is followed to establish the corresponding plant dynamics. As the medium for transmitting power, the compressed air in the control chamber must generate enough force to actuate the relay piston. The physical state of the compressed air changes with the dilating control chamber in the process. Generally speaking, because braking is relatively fast and fierce, the variation of the air in the control chamber can be regarded as adiabatic, and if the temperature difference between the incoming air and original air of the chamber is assumed to be negligible, the pneumatic polytropic process of an open system with a variable internal mass can be used to express the relationship at the two states


pr

Vr mar

n


¼ pr0

V r0 mar0

n ¼ const:

ð1Þ

where pr0 , Vr0 and mar0 are the pressure, volume and mass at the initial condition, respectively, and pr , Vr and mar are the corresponding states at equilibrium. The constant polytropic exponent n can be rounded to 1.4 without significant loss of accuracy. Differentiating Eq. (1) with respect to time,

p_ r ¼

npr np _ ar  r V_ r m mar Vr

ð2Þ

_ ar is the mass gradient in the control chamber which equals to the mass flow transiting the orifice of the inlet or where m _ ar . Theoretically, Gar is a funcrelease valve per unit time. Define the mass flow rate into the chamber as Gar , one has Gar ¼ m tion of the effective orifice area. However, because high-speed switch valve does not have the capability to vary orifice area continuously as a kind of on-off valve, the valve opening duration in a period, which is decided by PWM duty cycle, is usually used to regulate the Gar when high-speed switch valve is employed. Switch valve can simulate the proportional valve through adjusting PWM duty cycle. Defining a virtual variable AE that represents the effective orifice area of the equivalent proportional valve as

(

AE ¼ f ðdIR ; dOR Þ ¼

dIR ; ð0 < dIR < 1Þ _ ðdOR ¼ 0Þ Amax E

ð3Þ

Amax dOR ; ð0 < dOR < 1Þ _ ðdIR ¼ 0Þ E

where dIR and dOR are PWM duty cycles of the inlet valve and release valves, respectively. Amax is the maximum effective E orifice area. According to the formulation between the gas flow and orifice area it can be shown that

Gar ¼

8  1=ðn1Þ  1=2 > 2 2n > ; ðAE P 0Þ ^ ðpr =ps 6 0:518Þ > T a Rðnþ1Þ > cd ps AE  nþ1 > > >   > 1=2 > n½ðpr =ps Þ2=n ðpr =ps Þðnþ1Þ=n  > > > ; ðAE P 0Þ ^ ðpr =ps > 0:518Þ < cd ps AE  T a Rðn1Þ=2

ð4Þ

 1=ðn1Þ  1=2 > > 2 2n > p A ; ðAE < 0Þ ^ ðpa =pr 6 0:518Þ c E  nþ1 d > r T R ð nþ1 Þ a > > >  1=2 > > 2=n ð nþ1 Þ=n >  > > cd pr AE  n½ðpa =pr Þ ðpa =pr Þ ; ðAE < 0Þ ^ ðpa =pr > 0:518Þ : T a Rðn1Þ=2 1 Inlet port 2 Release port

2

3 Action port 1

2

3

3

1

1

Fig. 2. Piston position and mode of action.

Initial position Centre position Terminal position 3 2

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401

5

with cd being the gas orifice flow coefficient, ps the pressure of supply air, pa the discharge atmospheric pressure, R the specific gas constant, and, based on the assumption before, Ta the absolute temperature in the control chamber. Constant 0.518 is a critical ratio of low-to-high pressure at the two sides of the orifice. When greater than 0.518, the flow is subsonic. Otherwise the flow is supersonic and the corresponding dynamics is complex which is oftentimes the case when air undergoes throttling. Relay valve piston moves under the pressure of the control chamber. Assume that it is located at the initial position shown in Fig. 2, the valve will experience several different dynamic processes. Using Newton’s Second Law of Motion with the coordinate system affixed in Fig. 1 to consider the (force) equilibrium of the piston



mr €xr ¼ Ar pr  Arl pc  F fr ; 0 6 xr 6 xrm ðmr þ mr1 Þ€xr ¼ Ar pr  Arl pc  K r xr  K r x0r  F fr1 ; xrm 6 xr 6 xrt

ð5Þ

where xr is the displacement of valve piston, Ar is the effective area of the control chamber, Ar1 is the effective area of the load chamber, Kr is the stiffness of the reset spring, Kr x0r represents spring preload, and Ffr is the friction between the piston and valve body, which is one of the primary sources of nonlinearity. Friction is generally considered as a function of position and velocity [29–31]. In this paper, the friction between piston and the control chamber will change with the servicing time goes on, because they are closely jointed at initial mounting to avoid air leak which lead to large vertical force, but with the continue movement and wearing the vertical force decrease gradually. Based on that, the friction is calculated by the below expression for that it is conducive to analyze the influence of friction to system nonlinear dynamic

F fr ¼ signðx_ r Þ  lF v

ð6Þ

with Fv being the vertical force and l the dynamic friction coefficient. The effective air flow area of the relay valve denoting AR , can be calculated by



AR ¼

C ro ðxr  xrm Þ; 0 6 xr 6 xrm C ri ðxr  xrm Þ; xrm 6 xr 6 xrt

ð7Þ

where Cri and Cro are the perimeters of the ring-like inlet orifice and release orifice, xrm is the center position that the release port is just closed and inlet port just begin to open. Combining with the balance equation in Eq. (5), it is understood that as the load pressure increases, the feedback effect on the piston tends to close the relay valve by decreasing AR . Define Gac as the mass flow rate into the cylinder through the relay valve. By replacing pr in Eq. (4) with pc , which is the pressure of the load chamber, and replacing AE with AR , Gac can be determined. Due to the short distance between the relay valve and wheel cylinder, the throttling effect of the connection pipeline is neglected and the pressure in cylinder is assumed to equal to pc . Correspondingly, the principle of Eq. (2) is also employed to describe the varying process of air state in the wheel cylinder. In practice, the wheel cylinder moves by a small distance and then stop when the caliper touches the brake disc. Therefore

p_ c ¼

npc np _ ac  c V_ c m mac Vc

ð8Þ

mc €xc ¼ Ac pc  K c xc  K c x0c  F fc

ð9Þ

where xc is the displacement of the wheel cylinder piston, pc0 , Vc0 and mac0 are the pressure, volume and air mass at the initial condition, respectively, pc , Vc and mac are the states of equilibrium. Kc is the stiffness of the wheel cylinder reset spring, Kc x0c represents spring preload, Ffc is the equivalent friction. In addition, such relationships are dictated by the configuration of the system as

V r ¼ V r0 þ Ar xr ; 0 6 xr 6 xrt

ð10Þ

V c ¼ V c0 þ Ac xc  Ar xr ;

ð11Þ

0 6 xr 6 xrt ; 0 6 xc 6 xct

2.2. System nonlinearity The model build in the previous section is simulated in Matlab/Simulink to characterize system nonlinearity using the system parameters tabulated in Table 1, where VS is the reference and change of Vc0 is to be calculated. As the dominant force of dissipation in the relay valve, friction between the piston and the control chamber is sensitive to structural variation. After having undergone through poor working conditions, the relaxation of the seal ring will result in a dropping in friction and render states of nonlinear response. As commercial vehicles have different wheel cylinders of different piping arrangement and initial load chamber volume, limit-cycle responses are prevalent. Thus, two important parameters Fv and Vc0 are selected to analyze their impact on the system dynamics. Fig. 3 shows the transient of pressure increase when the inlet valve is fully opened. It can be seen in Fig. 3(a) that the pressure fluctuates violently up to the target with the Fv decreasing. In Fig. 3(b), where Fv is set to be 500 N and Vc0 varies from the initial value to twice its reference value at Vc0 ¼ 2VS , oscillations are the predominant feature.

6

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401 Table 1 The parameters used in the system. Parameters

Value/Unit

Parameters

Value/Unit

ps pa Ta R n

0.8 MPa 0.1 MPa 300 K 287.1 J/(kgK) 1.4 1.025 kg/m3 3.25  103 m 5.5  103 m 2.18  103 m 0.046 kg 2.2  105 m3

Ar Kr C ri C ro mc VS Ac Kc xct x0t

3.2  103 m2 2500 N/m 8.48  102 m 6.28  102 m 0.65 kg 1.5  105 m3 9.5  103 m2 2150 N/m 0.012 m 0.041 m 0.73

qa xrm xrt x0r mr V r0

(a) Nonlinear response with Fv varying

l

(b) Nonlinear response with Vc0 varying

Fig. 3. Nonlinear EPBS responses under open-loop.

Pressure stabilizes eventually at the maximum pressure under the open-loop condition. However, in closed-loop proportional control in Fig. 4, oscillations occur both in the transient and steady-state owing to the feedback mechanism. It is also seen in Fig. 4(a) and (b) that the oscillation frequency is higher when Fv is smaller or Vc0 is larger. The oscillations can be explained by the displacement of the relay valve piston in Fig. 4(c) and (d). Parameter variation leads to rapid jerking of the valve piston and inadvertently induces pressure chattering which is a mode of nonlinear response. This calls for the deployment of nonlinear controllers. 3. Nonlinear controller design High Frequency chatter in nonlinear system is difficult to deal with using feedback control. An approach effective for addressing nonlinear oscillations is to decrease the frequency gradually to zero [32,33]. The two-component nonlinear control strategy depicted in Fig. 5 follows the idea. One component is the adaptive feedforward amplitude-phase regulator, which uses a pair of weighted orthogonal harmonics as input. The other is the state feedback controller based on a high gain observer. Conditions are used to define the logic rule needed to coordinate the two components. The first condition which depends on the low frequency component of error is used to trigger the time-frequency analysis. The second condition enable the adaptive amplitude-phase regulation and the third condition is used to add the middle state feedback into the control action, they rely on the judgement of the frequency value of high frequency component of error. The reason why set these logical rules is elaborated in the followings. 3.1. Adaptive feedforward amplitude-phase regulator Generally, state feedback control method is effective to give satisfactory tracking performance. However, with EPBS demonstrating nonlinearities, high frequency oscillations do not give enough time for a state feedback controller to operate because of the limitation of micro-ship computing capability in practice. Moreover, the time delay in every control cycle can deteriorate control stability. Therefore, feedforward control is preferred. Feedforward amplitude-phase regulator is usually used in hydraulic vibration generator systems for enhancing tracking performance or harmonic cancellation [34]. As a kind of auxiliary correcting method, it often cooperates with feedback controller to further diminish the control error led by phase lag. The benefits are that model estimation is not required and that

7

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401

(a) Nonlinear response with Fv varying

(b) Nonlinear response with Vc0 varying

(c) Displacement response of relay valve piston when Fv = 200N

(d) Displacement response of relay valve piston with Vc0 = 2VS

Fig. 4. Nonlinear EPBS responses under closed-loop proportion control with step input.

r e

e sin(2 ft)

rc

w0 cos(2 ft)

u

Kp1

w1

Pneumatic Electric Braking System High Gain Observer

Kp2 f

X

Condition 3

pc

xr

LMS eL

Condition 2

Fast Fourier Transform Condition 1

eH

Low Pass Filter High Pass Filter

Time-Frequency Analysis

Fig. 5. Schematic of the nonlinear controller.

the LMS algorithm used for updating filter weights is fast running in micro-ship. Fig. 6 gives the schematic of a typical amplitude-phase regulator. After the state or output being feedback-controlled, the closed-loop system can be regarded as a linear minimum phase system. If defining a sinusoid as the system input

x ¼ AI sinðxtÞ where AI is the amplitude, and x is the angular frequency, then the system response is

ð12Þ

8

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401

x

State or Output Feedback

System

y

Closed-Loop System Synthetic Input

x

w0

xc

State or Output Feedback

w1

System

y

Closed-Loop System

Fig. 6. Schematic of amplitude-phase regulator.

y ¼ AO sinðxt  uÞ

ð13Þ

with AO being the amplitude of the system response and u the phase lag. To reduce the error by phase lag, the input can be modulated as a synthetic input

xSI ¼ AI sinðxt þ uÞ ¼ cosu AI sinxt þ sinu AI sinðxt þ 90 Þ |fflffl{zfflffl} |fflfflfflfflffl{zfflfflfflfflffl} |fflffl{zfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} w0

x

w1

ð14Þ

xc

meaning that the introduction of an extra compensator xc (phase shifting 90° leftwards of the original system input x) and weighted calculation can solve these problems. The same idea is also applicable to chatter suppression. As can be seen in Fig. 4, the violent chattering caused by smaller Fv or larger Vc0 is not conformal to sinusoid but rather oscillating in a fixed frequency over a short time. A reverse oscillation with a proper frequency, amplitude and phase ahead can effectively counteract the chatter. A feasible adaptive algorithm is one that updates the weighted coefficients in every control period by timely adjusting the amplitude and phase. Frequency is obtained by applying Fast Fourier Transform (FFT) to a windowed feedback signal sequence. To calculate the compensator, the amplitude-phase regulator in Fig. 6 is incorporated into Fig. 5 to get

rc ¼ WX T

ð15Þ

where W ¼ ½w0 ; w1  is the coefficients vector to be updated,X ¼ ½sinð2pf sÞ; cosð2pf sÞ is the synthetic input vector including a pair of orthogonal harmonic mutually as the base. The key parameter is the frequency f used in X which comes from the time frequency analysis to the feedback signal pc . It has

ep ðkÞ ¼ r ðkÞ  pc ðkÞ

ð16Þ

here ep ðkÞ is the error between the desired output pressure and system actual output at time k, the data sequence including

N times error makes up the error vector as ep ðkÞ ¼ ep ðkÞ; ep ðk  1Þ;    ; ep ðk  N þ 1Þ , it is defined as first-in-first-out to ensure that a fixed length of datum is processed for frequency information. eLp ðkÞ is the component containing low frequency information and eHp ðkÞ is the domain holding high frequency, which can be computed through a low pass filter (LPF) and a high pass filter (HPF), respectively, as follows



 eLp ðkÞ ¼ eLp ðkÞ; eLp ðk  1Þ;    ; eLp ðk  N þ 1Þ ¼ LPF ep ðkÞ

ð17Þ



 eH p ðkÞ ¼ eHp ðkÞ; eHp ðk  1Þ;    ; eHp ðk  N þ 1Þ ¼ HPF ep ðkÞ

ð18Þ

the high frequencies component eHp ðkÞ is used to calculate the frequency spectrum via FFT that is characteristic of the chatter caused by system nonlinearity. Being able to resolve chatter frequency with precision also helps avoid the disturbance of low frequency error due to phase-lag or load variation. Noting that the frequency spectrum acquired by FFT is a function with  that abscissa is frequency and ordinate is amplitude, that means F ðf Þ ¼ FFT eHp ðkÞ . When chattering, the frequency value that the maximum amplitude mapping is the chatter frequency obviously. But in normal situation, it is hard to distinguish the frequency information of noise and high frequency disturbance, even taking the frequency of the noise as the wrong value will make the system unstable. To address this issue, the maximum amplitude and the average amplitude of Fðf Þ should be compared to decide whether start to suppress the chatter. Denote that AMmax is the maximum amplitude value of the certain frequency, whereas the AMave is the average amplitude value of the remain frequency domain which taking out the maximum amplitude value, it has

AMmax ¼ maxfFð f Þg AMave ¼

Pf max 0

Fð f Þ  maxfFð f Þg Nf  1

ð19Þ ð20Þ

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401

f ¼ F1 ð AMmax Þ

9

ð21Þ

where Nf is the number of frequencies be discretized after FFT. Based on the white noise hypothesis, if the chatter do not happen, the AMmax approximates to the AMave , if it satisfies the condition AMmax > 2AMave , we think that the chatter happens, then the frequency value f which the maximum amplitude matching will be sought out. Least mean square (LMS) algorithm is adopted to update the weighted coefficients. Requiring only multiplication and addition operations, LMS is explored for realizing real-time control. The updating formula is

W ðk þ 1Þ ¼ W ðkÞ þ g  ep ðkÞ  X ðkÞ

ð22Þ

where g is the step size taken at each iteration. When chosen properly, adaptation noise due to error in the gradient estimate can be averaged out. When adapting with LMS adaptive filtering algorithm on stationary stochastic processes, the expected value of the weight vector converges to a Wiener optimal solution. 3.2. State feedback control and high gain observer When high frequency chatter is assuaged, system pressure will not go to steady state immediately but rather fluctuate with a low frequency. State feedback control method is preferred which used in second stage to continue suppress it, due to the state feedback controller has better adjusting effect for phase correction than proportional control leading to rapid vibration control results. But in reality, there are situations that not all the states values are available considering the high cost and difficulty in mounting sensors. It is therefore necessary to estimate state variables. Indeed, designing nonlinear observer common for developing precise and robust controllers of pneumatic system that are employed in many occasions [35]. High-gain observer is a useful tool in the design of feedback control for nonlinear systems, which can be applied to both SISO (Single Input Single Output) and MIMO (Multiple Input Multiple Output) systems. Khalil [36] gave a comprehensive summary on observer design, making it convenient to acquire a good performance observer through adjusting the parameters. Using the model from Section 2 and setting x1 ¼ pc , x2 ¼ xc , x3 ¼ x_ c , x4 ¼ xr , x5 ¼ x_ r , x6 ¼ pr , the system model is

8 x_ 1 > > > > > x_ 2 > > > < x_ 3 > x_ 4 > > > > > x > _5 > : x_ 6

¼ f 0 ðx1 ; x2 ; x3 ; x4 ; x5 Þ ¼ x3 ¼ f 1 ðx1 ; x2 ; x3 Þ ¼ x5 ¼ f 2 ðx1 ; x4 ; x5 ; x6 Þ ¼ f 3 ðu; x4 ; x5 ; x6 Þ

ð23Þ

The system functions of the high-gain observer can be derived as follows

8 ^x_ ¼ f 0 ð^x1 ; ^x2 ; ^x3 ; ^x4 ; ^x5 Þ þ ae 1 ðx1  ^x1 Þ > > 1 > 1 > > a > _ > > ^x2 ¼ ^x3 þ e22 ðx1  ^x1 Þ > 1 > > > > a > < ^x_ 3 ¼ f 1 ð^x1 ; ^x2 ; ^x3 Þ þ e33 ðx1  ^x1 Þ 1

> ^x_ 4 ¼ ^x5 þ a44 ðx1  ^x1 Þ > > e1 > > > > ^_ > x5 ¼ f 2 ð^x1 ; ^x4 ; ^x5 ; ^x6 Þ þ ae55 ðx1  ^x1 Þ > > > 1 > > > : ^x_ 6 ¼ f ðu; ^x4 ; ^x5 ; ^x6 Þ þ a66 ðx1  ^x1 Þ 3 e

ð24Þ

1

T Define x ¼ ½x1 ; x2 ; x3 ; x4 ; x5 ; x6 T , b x ¼ ½b x1; b x2; b x3; b x4; b x5 ; b x6  , e ¼ x  b x ¼ ½e1 ; e2 ; e3 ; e4 ; e5 ; e6 T is the estimated error, and

ai ði ¼ 1; 2;    ; 6Þ ande1 are parameters of the high gain observer to be designed. The error equations are
 8 ^ > a > > e_ 1 ¼  e11 e1 þ d0 x; x > > > > > > e_ 2 ¼  ae22 e1 þ e3 > > > 1 >
 > > ^ > a > 3 _ > ¼  e þ d x; x e 3 1 1 < e3 1

> e_ 4 ¼  ae44 e1 þ e5 > > 1 >
 > > > ^ > a 5 > _ e ¼  e þ d x; x > 5 1 2 5 > e1 > > >
 > > ^ > > : e_ 6 ¼  ae66 e1 þ d3 x; x 1

ð25Þ

10

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401

b5; x b 6 Þ, d1 ðx; b in which, d0 ðx; b x Þ ¼ f 0 ðx1 ; x2 ; x3 ; x4 ; x5 ; x6 Þ  f 0 ð b x1 ; b x2 ; b x3 ; b x4 ; x x Þ ¼ f 1 ðx1 ; x2 ; x3 Þ  f 1 ð b x1; b x2; b x 3 Þ, d2 ðx; b xÞ ¼ x1; b x4 ; b x5 ; b x 6 Þ, d3 ðx; b x Þ ¼ f 3 ðu; x4 ; x5 ; x6 Þ  f 3 ðu; b x4; b x5; b x 6 Þ, and Eq. (22) can be described as e_ ¼ Ae þ f 2 ðx1 ; x4 ; x5 ; x6 Þ  f 2 ð b with

2

a1 =e1 6 a2 =e2 6 1 6 6 a3 =e31 6 A¼6 4 6 a4 =e1 6 4 a5 =e51 a6 =e

6 1

0

0 1 0 0 0

0 0 0

0

0 0 1

0

0 0 0

0

0 0 0

3

3 2 ^Þ d0 ðx; x 7 7 6 07 6 0 7 7 7 6 ^ 7 6 07 7; - ¼ 6 d1 ðx; xÞ 7 7 7 6 07 6 0 7 7 7 6 4 d2 ðx; x ^Þ 5 05 ^Þ 0 d3 ðx; x

0 0 0 0

ð26Þ

The estimated state needs time to approach the actual state of the system, thus di ðx; b x Þ is not zero but bounded. As time elapses, error e converges to a compact set and supx2R jGo ðjxÞj will be arbitrarily small if ai ande1 are properly chosen, Go ðjxÞ is the transfer function from di to b x [36]. As di ðx; b x Þ is infinitely small, so - is bounded. When the derivative of the Lyapunov function of the system is less than zero, Lyapunov stability is satisfied. To guarantee robust performance of the observer, the Lyapunov function is selected as V ¼ eT Pe, the derivative of V is

  T V_ ¼ e_ Pe þ eT Pe_ ¼ eT AT P þ PA e þ eT P- þ -T Pe

ð27Þ

where P is a symmetric positive definite matrix. An H1 criteria for k Ge ðjxÞ k1 < c is

V_ þ eT Qe  c2 -T - 6 0

ð28Þ

where Q is a positive definite weight matrix, Ge ðjxÞ is the transfer function mapping - to e. The solution for Eq. (25) can be rearranged by solving the linear matrix inequality (LMI) in the followings

  V_ þ eT Qe  c2 -T - ¼ eT AT P þ PA þ Q e þ eT P- þ -T Pe  c2 -T - 6 0 " # 

 e e P AT P þ PA þ Q 6 0 ( ) e 60 ½  K () ½ e -  P c2 I -

ð29Þ

when K is a negative definite matrix with properly selected ai ande1 , the inequality in Eq. (26) is satisfied and supx2R jGe ðjxÞj 6 c , thus indicating a robust observer design is realized. 3.3. Synthetic nonlinear controller When chatter is detected by pressure sensor, the controller is switched to active chatter suppression mode, because prior to that the proportional control action is adequate for pressure tracking. So, a switch strategy is needed for managing the many scenarios for control. Two conditions need to be satisfied to start the active chatter suppression control mode. One is that the system output is approaching the target which is the desired steady state where system chattering do not significantly impact control precision. The other is that frequency should be beyond a threshold because the state feedback control is difficult to handle chatter at high frequency. The nonlinear control strategy is depicted in the flow chart in Fig. 7. Condition (1) is the error in the low frequency domain, eLp ðkÞ 6 T 0 , which ensures the system output runs within a desired range without influencing by high frequency and large amplitude chattering. To calculate chatter frequency, the error in the low frequency domain eLp ðkÞ just as phase lag or disturbance external is eliminated, and the remained part eHp ðkÞ is used only to implement FFT to get frequency f, then f P F 0 is regarded as Condition (2). Summarizing the ideas conveyed in Figs. 5 and 7, the control input is synthesized as

  8 T0 _ ð0 6 f 6 F0 Þ > < K p1 ep ðkÞ; eLp ðkÞ P   u ¼ K p1 ep ðkÞ þ K p2 ^x_ r ; eLp ðkÞ 6 T0 ^ ðF0 6 f 6 F1 Þ >     : K p1 r c þ ep ðkÞ ; eLp ðkÞ 6 T0 ^ ðf P F1 Þ

ð30Þ

where Kp1 , Kp2 is the proportional coefficients at different stage. 4. Simulation and experiments The performance of the proposed nonlinear controller is evaluated numerically as well as physically that simulates different working conditions. This is done by varying step response and sinusoid tracking which are situations EPBS systems typically encountered.

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401

11

Fig. 7. Flow chart for nonlinear control strategy.

4.1. Simulation and verification Two kinds of reference trajectories are designated in the simulation. One is step response and the other is sinusoidal trajectory, which are representative of emergency braking and gentle braking, respectively. The controller is built in Matlab/ Simulink using S-Function and proper controller parameters are determined through trial-and-error. With repeated simulations, the following 2 sets of optimal parameters are obtained from considering the best tracking performances. The parameters of observer are

e1 ¼ 0:1, a1 ¼ 0:8, a2 ¼ a4 ¼ 1  109 , a3 ¼ a5 ¼ 1  108 , a6 ¼ 2  106 . The feedback controller

parameters are K p1 ¼ 5  1011 , K p2 ¼ 5  106 , N ¼ 30, T 0 ¼ 1:5  105 , F 0 ¼ 50, F 1 ¼ 2. The initial weights are set to be w00 ¼ w10 ¼ 4  105 . Integration time step is one millisecond and the low pass filter matching this time step is designed as follows

GðzÞ ¼

b1

a1 z1 þ a2 z2 þ b2 z2 þ b3 z3

z1

ð31Þ

where a1 ¼ 0:202, a2 ¼ 0:122, b1 ¼ 1, b2 ¼  0:899, and b3 ¼ 0:023. It is designed requiring that the EPBS response time subject to the largest step to be twenty milliseconds. The low frequency error component eLp ðkÞ is obtained through filtering the error sequence eðkÞ, and the high frequency error component is computed using eHp ðkÞ ¼ ep ðkÞ  eLp ðkÞ. Fig. 8(a) gives the step response of EPBS when the vertical force Fv is decreased to 200 N considering the wear of the relay valve piston and relaxation of the seal ring. Fig. 8(b) gives the result when the initial load chamber volume Vc0 is varied to twice of its reference value. The system is seen to chatter once the step amplitude is beyond a threshold. However, under the nonlinear controller, chatter is suppressed to a low frequency oscillation with gradually decreasing amplitude till the target value is reached. Dampened oscillations are observed in all the controlled cases. Fig. 8(a) shows that chatter is reigned in within 0.05 s, while the time for Fig. 8(b) is 0.15 s.

12

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401

(b) Step response with Vc0 = 2VS

(a) Step response with Fv = 200N Fig. 8. Step response after control.

(a) Step response with Fv = 200N

(b) Step response with Vc0 = 2VS

Fig. 9. State estimated comparison in step response after control.

Fig. 9 presents the estimated piston velocity. The chatter frequency is so high that the estimated state does not track the real state at all initially. After the active adaptive amplitude-phase control is deployed, the chatter frequency decreases so that the estimated state can track the real state and the state feedback controller works to reduce oscillations. It is the reason why employing the state feedback control only does not overcome high frequency chatter. Fig. 10 presents the result of sinusoid tracking. The desired sinusoid can simulate moderate-varying braking mode such as when a commercial vehicle running a long downhill. Chatter suppression takes less than 0.3 s subject to the condition regardless if Fv is smaller or Vc0 becomes larger, it satisfies the braking performance required of commercial vehicles. It eventually achieves the desired tracking performance, thus validating the effectiveness of the proposed control strategy.

(a) Sinusoid tracking response with Fv = 200N

(b) Sinusoid tracking response with Vc0 = 2VS

Fig. 10. Sinusoid tracking response after control.

13

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401

4.2. Experiments and results Fig. 11 shows the indoor test bench built to validate the controller design. A pressure sensor is mounted in the wheel cylinder to measure the output EPBS pressure. The proposed control algorithm is compiled in C-language in a brake control unit that includes a micro-chip and several power amplifier chips. The micro-chip exerts control by adjusting the solenoid (inlet and release) valves through PWM. The brake control unit can communicate with the electronic control unit (ECU) via controller area network (CAN) to get object instructions such as desired braking intensity or pressure value. In this physical validation a host computer and NI PXI-1071 are employed to replace the ECU to send messages to and collect pressure information from brake control unit. The host computer also displays pressure curve in real-time. It is difficult to manipulate the friction between the piston and the control chamber. In other words, it is practically impossible for designing a braking control design that accommodate wear and relaxation induced EPBS nonlinearities through changing Fv alone. In contrast, varying of Vc0 can be easily handled by using different lengths of pipeline between the relay valve and wheel cylinder. Thus, the experiment is implemented by setting Vc0 ¼ 2VS . In order to evaluate control performance, the control results under the proportional control is also presented for comparison. The proportional coefficient is set at K p ¼ 3  1011 . Fig. 12 presents the testing results under the proportional control while the results under the proposed control method is found in Fig. 13. Compare the two sets of control results, one sees that although the proportional coefficient Kp is selected to be smaller than that of the nonlinear controller Kp1 , chatter still emerges subject to the proportion control at the first step input and the fifth step at t = 0.8 s in Fig. 12(a). Chatter oscillations are of a long duration (about 0.4 s) in Fig. 12(b). Generally speaking, as dictated by linear control theory, larger the proportional coefficient is incorporated, faster the corresponding system dynamic would respond. However, with the incorporated nonlinearities dominating, the system is predominantly in a state of instability despite of the large proportional coefficient. The proposed nonlinear controller is seen in in Fig. 13 to put system chattering under control without deteriorating the dynamic response despite of the bigger proportional coefficient Kp1 chosen.

Host computer

Low-voltage power supply

NI PXI-1071

Air supply bump

CAN Air holder

Pressure sensor Wheel cylinder

Relay valve

Brake control unit

(b) Structure of test bench

(a) Experiment scene Fig. 11. EPBS test bench.

(a) Step response

(b) Sinusoid tracking

Fig. 12. Experimental results under the proportional control.

14

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401

(a) Step response

(b) Sinusoid tracking

Fig. 13. Experimental results under the proposed control method.

Above all, the results have shown that the proposed method can achieve satisfied control effectiveness not only in simulation, but also in real plant. 5. Conclusion A nonlinear controller has been developed to address the high frequency chatter of EPBS induced by wear, aging of moving parts, or change of service environment. The controller includes three parts: one is an adaptive feedforward amplitudephase regulator based on LMS algorithm to reduce the high frequency pressure response oscillation to a low frequency domain, the other is output feedback controller based on a high gain observer is used to overcome the low frequency oscillate to steady state, the last is a logic rule to make sure that the two controllers are specially designed for pressure oscillation suppress in high and low frequency domain respectively and switching smoothly. The system model is built to analyse the system nonlinearities and the controller design process is introduced. A series of simulations and experiments are conducted to evaluate the reliability and feasibility of proposed methods. Results showed that the proposed method can suppress the oscillation of EPBS gradually till to the steady and track the desire curve closely at the same time, which ensure the braking safety of commercial vehicle in extreme condition. Furthermore, this method can also be used to other system which encountering fluctuation in high frequency, and more detailed research just likes multiple frequency domain segmentation and parallel controllers can be conducted to improve the instable suppression as PHEB system shown. Base on the thought, advanced time-frequency skills just as wavelet transform and Hilbert-Huang transform should to be researched in the future, which identify the nonlinear chatter as soon as possible and the chatter suppress process will be shorter. Acknowledgements The authors are very grateful to the China government by the support of this work through the National Key Research and Development Program of China (Grant No. 2017YFB0103502), and the National Natural Science Foundation of China (Grant No. 51675293). References [1] G. Morrison, D. Cebon, Sideslip estimation for articulated heavy vehicles at the limits of adhesion, Veh. Syst. Dyn. 54 (11) (2016) 1601–1628. [2] G. Morrison, D. Cebon, Combined emergency braking and turning of articulated heavy vehicles, Veh. Syst. Dyn. 55 (5) (2017) 725–749. [3] B. Zhu, Y. Feng, J. Zhao, Model-based pneumatic braking force control for the emergency braking system of tractor-semitrailer, (No. 2018-01-0824) (2018) SAE Technical Paper. [4] H. Zheng, S. Ma, Y. Liu, Vehicle braking force distribution with electronic pneumatic braking and hierarchical structure for commercial vehicle, Proc. Inst. Mech. Eng., Part I: J. Syst. Control Eng. 232 (4) (2018) 481–493. [5] F. Ning, Y. Shi, M. Cai, Y. Wang, W. Xu, Research progress of related technologies of electric-pneumatic pressure proportional valves, Appl. Sci. 7 (10) (2017) 1074–1789. [6] J. Wu, X. Wang, L. Li, Y. Du, Hierarchical control strategy with battery aging consideration for hybrid electric vehicle regenerative braking control, Energy 145 (2018) 301–312. [7] J. Zhang, X. Chen, P. Zhang, Integrated control of braking energy regeneration and pneumatic anti-lock braking, Proc. Inst. Mech. Eng., Part D: J. Automobile Eng. 224 (5) (2010) 587–610. [8] H. Zhang, J. Wang, Active steering actuator fault detection for an automatically-steered electric ground vehicle, IEEE Trans. Veh. Technol. 66 (5) (2016) 3685–3702. [9] Z. Wang, G. Li, Q. Wu, J. Xu, Research on pressure characteristics of vehicle air braking system with leakage from pipeline, Appl. Mech. Mater., Trans Tech Publ. 157 (2012) 608–611. [10] S. Bharath, B.C. Nakra, K.N. Gupta, Mathematical model of a railway pneumatic brake system with varying cylinder capacity effects, J. Dyn. Syst. Meas. Contr. 112 (3) (1990) 456–462. [11] H. Zhang, J. Wu, W. Chen, Y. Zhang, L. Chen, Object oriented modeling and simulation of a pneumatic brake system with ABS, in: IEEE Intelligent Vehicles Symposium, 2009, pp. 780–785.

X. Wu et al. / Mechanical Systems and Signal Processing 135 (2020) 106401

15

[12] J.I. Miller, D. Cebon, Modelling and performance of a pneumatic brake actuator, Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci. 226 (8) (2012) 2077– 2092. [13] W. Wei, Y. Hu, Q. Wu, X. Zhao, J. Zhang, Y. Zhang, An air brake model for longitudinal train dynamics studies, Veh. Syst. Dyn. 55 (4) (2017) 517–533. [14] P. Karthikeyan, C.S. Chaitanya, N.J. Raju, S.C. Subramanian, Modelling an electropneumatic brake system for commercial vehicles, IET Electr. Syst. Transp. 1 (1) (2011) 41–48. [15] S. Ramaratham, A mathematical model for air brake systems in the presence of leaks, Doctoral dissertation, A&M University, Texas, 2008. [16] J.I. Miller, L.M. Henderson, D. Cebon, Designing and testing an advanced pneumatic braking system for heavy vehicles, Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci. 227 (8) (2013) 1715–1729. [17] D.B. Sonawane, K. Narayan, V.S. Rao, S.C. Subramanian, Model-based analysis of the mechanical subsystem of an air brake system, Int. J. Automot. Technol. 12 (5) (2011) 697–704. [18] J. Wu, H. Zhang, Y. Zhang, L. Chen, Robust design of a pneumatic brake system in commercial vehicles, SAE Int. J. Commer. Veh. 2 (2009) 17–28. [19] S. Mithun, S. Mariappa, S. Gayakwad, Modeling and simulation of pneumatic brake system used in heavy commercial vehicle, IOSR J. Mech. Civ. Eng. 11 (1) (2014) 1–9. [20] P. Mishra, V. Kumar, K.P.S. Rana, An online tuned novel nonlinear PI controller for stiction compensation in pneumatic control valves, ISA Trans. 58 (2015) 434–445. [21] Y.S.R. Kumar, D.B. Sonawane, S.C. Subramanian, Application of PID control to an electro-pneumatic brake system, Int. J. Adv. Eng. Sci. Appl. Math. 4 (4) (2012) 260–268. [22] P. Karthikeyan, D.B. Sonawane, S.C. Subramanian, Model-based control of an electropneumatic brake system for commercial vehicles, Int. J. Automot. Technol. 11 (4) (2010) 507–515. [23] H. Jing, Z. Liu, H. Chen, A switched control strategy for antilock braking system with on/off valves, IEEE Trans. Veh. Technol. 60 (4) (2011) 1470–1484. [24] C. Yang, S. Du, L. Li, S. You, Y. Yang, Y. Zhao, Adaptive real-time optimal energy management strategy based on equivalent factors optimization for plugin hybrid electric vehicle, Appl. Energy 203 (2017) 883–896. [25] C. Yang, X. Jiao, L. Li, Y. Zhang, Z. Chen, A robust H1 control-based hierarchical mode transition control system for plug-in hybrid electric vehicle, Mech. Syst. Sig. Process. 99 (2018) 326–344. [26] C. Yang, J. Song, L. Li, S. Li, D. Cao, Economical launching and accelerating control strategy for a single-shaft parallel hybrid electric bus, Mech. Syst. Sig. Process. 76 (2016) 649–664. [27] S.V. Natarajan, S.C. Subramanian, S. Darbha, K.R. Rajagopal, A model of the relay valve used in an air brake system, Nonlinear Anal. Hybrid Syst 1 (3) (2007) 430–442. [28] G.G. Kremer, Enhanced robust stability analysis of large hydraulic control systems via a bifurcation-based procedure, J. Franklin Inst. 338 (7) (2001) 781–809. [29] A. Alleyne, R. Liu, A simplified approach to force control for electro-hydraulic systems, Control Eng. Pract. 8 (12) (2000) 1347–1356. [30] C.C. De Wit, H. Olsson, K.J. Astrom, P. Lischinsky, A new model for control of systems with friction, IEEE Trans. Autom. Control 40 (3) (1995) 419–425. [31] W.S. Owen, E.A. Croft, The reduction of stick-slip friction in hydraulic actuators, IEEE/ASME Trans. Mechatron. 8 (3) (2003) 362–371. [32] B. Yang, C.S. Suh, Interpretation of crack-induced rotor non-linear response using instantaneous frequency, Mech. Syst. Sig. Process. 18 (3) (2004) 491– 513. [33] M. Liu, C.S. Suh, On controlling milling instability and chatter at high speed, J. Appl. Nonlinear Dyn. 1 (1) (2012) 59–72. [34] J. Yao, D. Di, G. Jiang, S. Gao, Acceleration amplitude-phase regulation for electro-hydraulic servo shaking table based on LMS adaptive filtering algorithm, Int. J. Control 85 (10) (2012) 1581–1592. [35] S.R. Pandian, F. Takemura, Y. Hayakawa, S. Kawamura, Pressure observer-controller design for pneumatic cylinder actuators, IEEE/ASME Trans. Mechatron. 7 (4) (2002) 490–499. [36] H.K. Khalil, High-gain observers in feedback control: Application to permanent magnet synchronous motors, IEEE Control Syst. Mag. 37 (3) (2017) 25– 41.